SLIDE 48 Steffen Axions etc. 44
Planck 2013 results XVI: Cosmological Parameters
D
at a given multipole. Combining Planck, WMAP polarization and the high-` experiments gives Neff = 3.36+0.68
−0.64
(95%; Planck+WP+highL). (74) The marginalized posterior distribution is given in Fig. 27 (black curve). Increasing Neff at fixed ✓∗ and zeq necessarily raises the ex- pansion rate at low redshifts too. Combining CMB with distance measurements can therefore improve constraints (see Fig. 27) al- though for the BAO observable rdrag/DV(z) the reduction in both rdrag and DV(z) with increasing Neff partly cancel. With the BAO data of Sect. 5.2, the Neff constraint is tightened to Neff = 3.30+0.54
−0.51
(95%; Planck+WP+highL+BAO). (75) Our constraints from CMB alone and CMB+BAO are compati- ble with the standard value Neff = 3.046 at the 1 level, giving no evidence for extra relativistic degrees of freedom. Since Neff is positively correlated with H0, the tension be- tween the Planck data and direct measurements of H0 in the base ΛCDM model (Sect. 5.3) can be reduced at the expense of high
- Neff. The marginalized constraint is
Neff = 3.62+0.50
−0.48
(95%; Planck+WP+highL+H0). (76) For this data combination, the 2 for the best-fitting model al- lowing Neff to vary is lower by 5.0 than for the base Neff = 3.046
- model. The H0 fit is much better, with ∆2 = −4.0, but there
is no strong preference either way from the CMB. The low-` temperature power spectrum does mildly favour the high Neff model (∆2 = −1.6) since Neff is positively correlated with ns (see Fig. 24) and increasing ns reduces power on large scales. The rest of the Planck power spectrum is agnostic (∆2 = −0.5), while the high-` experiments mildly disfavour high Neff in our fits (∆2 = 1.3). Further including the BAO data pulls the cen- tral value downwards by around 0.5 (see Fig. 27): Neff = 3.52+0.48
−0.45
(95%; Planck+WP+highL+H0+BAO). (77) The 2 at the best-fit for this data combination (Neff = 3.37) is lower by 3.6 than the best-fitting Neff = 3.046 model. While the high Neff best-fit is preferred by Planck+WP (∆2 = −3.3) and the H0 data (∆2 = −2.8 giving an acceptable 2 = 2.4 for this data point), it is disfavoured by the high-` CMB data (∆2 = 2.0) and slightly by BAO (∆2 = 0.4). We conclude that the tension between direct H0 measurements and the CMB and BAO data in the base ΛCDM can be relieved at the cost of additional neutrino-like physics, but there is no strong preference for this extension from the CMB damping tail. Throughout this subsection, we have assumed that all the
[Planck Collaboration, 1303.5076]
∆Neff = 3.62 + 0.5 - 3.046 = 1.074 @ 95% CL